On the extension of lattice-valued implications via retractions

Palmeira, Eduardo Silva; Bedregal, Benjamín R. C.; Fernández, Javier; Jurío, Aránzazu

doi:10.1016/j.fss.2013.07.023

Cited by 24 publications

(26 citation statements)

References 12 publications

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“…Also in this framework, we apply this method for extending QL-implications considering our previous study about extension of fuzzy implications described in [3].…”

Section: Methodsmentioning

confidence: 99%

“…Also in this framework, we apply this method for extending QL-implications considering our previous study about extension of fuzzy implications described in [3]. Consider an ordinary sublattice M of a bounded lattice L (i.e., M ⊆ L) and T a t-norm on M. Since a t-norm is particularly a function, it is natural to think if it is possible to extend T from M to L in order to obtain a new t-norm T E on L.…”

Section: Extension Methods Via Retractions (Emr)mentioning

confidence: 99%

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Some results on extension of lattice-valued QL-implications

2016

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Background: A very important issue in lattice theory is how to extend a given operator preserving its algebraic properties. For lattice-valued fuzzy operators framework, in 2008 Saminger-Platz presented a way to extend t-norms which was generalized by Palmeira et al. (2011) for t-norms, t-conorms, fuzzy negations and implications, considering the scenery provided by the (r, s)-sublattice. Methods: In this paper we investigated how to extend QL-implications and which properties of it are preserved by the extension method via retractions (EMR). Results:As results, we proved that properties (LB), (RB), (CC1), (CC2), (CC3), (CC4), (L-NP), (EP) and (IP) are preserved by EMR. Conclusions: However, the extension method via retractions fails in preserving the important properties (NP), (OP), (IBL), (CP), (P) and (LEM).

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“…Also in this framework, we apply this method for extending QL-implications considering our previous study about extension of fuzzy implications described in [3].…”

Section: Methodsmentioning

confidence: 99%

Section: Extension Methods Via Retractions (Emr)mentioning

confidence: 99%

Some results on extension of lattice-valued QL-implications

2016

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“…Also in this framework, we apply this method for extending QL-implications considering our previous study about extension of fuzzy implications described in [18].…”

Section: Extension Of Fuzzy Connectivesmentioning

confidence: 99%

“…[18] Under the same conditions as inTheorem 4.5, if I is an implication on M satisfying some of properties (LB), (RB), (CC4), (EP), (IP), (IBL) and (CP) then I E is an implication on L which satisfies the same properties.…”

mentioning

confidence: 94%

“…The pioneer work in this framework was published by Saminger-Platz et al in [19] which provides a method to extend a t-norm T from a complete sublattice M to a bounded lattice L. Later, we have developed in [16] an extension method to extend t-norms, t-conorms and fuzzy negations that generalizes the method proposed in [19] considering a modified notion of sublattice. Also, we have applied this method for fuzzy implications in [18].…”

Section: Introductionmentioning

confidence: 99%

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Extension of Lattice-valued QL-implications

Palmeira

Bedregal

2013

2013 2nd Workshop-School on Theoretical Computer Science

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The problem of extending function from a subset to the entire set can be considered for several operators in different branches of knowledge. We have provided a method to extend lattice-valued t-norms, t-conorms end fuzzy negations, in our previous investigations. In this paper, we apply this extension method for lattice-valued QL-implications and analyze its behavior. We also discuss about the relation between extension and conjugate of a given implication.

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